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BAGHDAD, Iraq (CNN) -- Iraq finally has names for its top jobs -- more than four months after its historic general election.

A political deadlock appears to have been broken Saturday, with Jawad al-Maliki asked to be prime minister-designate and form a new government.

Al-Maliki, a Shiite, was nominated a day earlier to replace interim Prime Minister Ibrahim al-Jaafari, who had been at the center of an impasse between Iraq's political parties. (Watch politicians break the stalemate -- 1:12)

Al-Maliki was asked to form an administration by Jalal Talabani, a Kurd, who was re-elected president by the parliament.

The prime minister-designate has a month to choose his ministers and present the list to parliament, acting parliament Speaker Adnan Pachachi told CNN.

If parliament votes in favor, the government will begin work. But if al-Maliki's Cabinet fails to gain support, someone else will be appointed to form a government, Pachachi said.

On Friday, the Shiite-led political bloc, the United Iraqi Alliance, put forward al-Maliki of the Dawa Party as its candidate to replace al-Jaafari.

Chosen as the new speaker of the Council of Representatives on Saturday was Sunni Arab politician Mahmoud al-Mashhadani. A Shiite, Khalid al-Attiya, and a Kurd, Aref Tayfour, were elected as his deputies.

A total of 266 members from the 275-seat body gathered for the key meeting, which had been delayed repeatedly and was finally held more than four months after the general election.

Before parliament convened, several members joined al-Maliki and U.S. Ambassador to Iraq Zalmay Khalilzad to iron out details on what would unfold.

Calls for unity

On Saturday before the parliamentary gathering, al-Maliki called for a government of national unity "to eradicate injustice that the Iraqis have suffered." He also urged Sunnis, Shiites, Kurds, Assyrians, Chaldeans and Yezidis to unite.

"We will work as one family to lead the political process, not based on our differences, sects or parties," al-Maliki said at a news conference before the parliament meeting.

A top Sunni Arab leader endorsed al-Maliki's selection.

"We will deal with Mr. [al-]Maliki, and we will work together in order to form a unity government," said Tariq al-Hashimi -- secretary-general of the Iraqi Islamic Party, the largest party in the most powerful Sunni Arab political bloc, the Iraqi Accord Front.

The main Kurdish grouping has not commented so far, but independent Kurdish politician Mahmoud Othman welcomed al-Maliki's nomination, Reuters reported.

Speaking from California, where he is attending an alternative energy event, President Bush said, "This historic achievement by determined Iraqis will make America more secure."

The formation of a new government has dealt a blow, Bush said, to "the enemies of freedom. ... The Iraqis are showing the world that democracy is worth the wait."

U.S. Secretary of State Condoleezza Rice called the selection of al-Maliki an "important milestone" for the Iraqis and said he was a man with whom the United States could do business.

"This is a good day for Iraq," Rice said in a conference call with reporters. "This is an important day for Iraq."

She said she had not met al-Maliki, but that Khalilzad knew him well.

"He is thought to be a strong figure, someone who is capable of getting things done," Rice said.

Sunnis, Kurds and secularists had opposed al-Jaafari as prime minister, saying weak leadership and sectarian strife had persisted under his watch. In addition, the Interior Ministry, led by a Shiite, was particularly criticized for allowing Shiite militias to infiltrate its ranks and patrol the streets.

On Saturday, al-Maliki addressed militias, saying "Arms should be in the hands of the government. There is a law that calls for the merging of militias with the armed forces."

Soldiers killed

Five U.S. soldiers were killed south of Baghdad on Saturday, the U.S. military said.

Four were killed by a roadside bomb that exploded near their vehicle while they were on patrol, the military said.

Later, the military announced the death of another soldier from wounds suffered in a roadside bombing. It is not clear whether all of the deaths resulted from the same bombing.

The number of U.S. service personnel killed in the Iraq war now stands at 2,387.

In addition, five bodies were found in Baghdad on Saturday, their hands tied behind their backs, shot in their heads. The bodies of a woman and two men were found in southern Baghdad, and the others were found in a western Baghdad neighborhood. Two roadside bombings targeting police patrols in eastern and central Baghdad wounded five officers.

Other developments

Sen. John Kerry said Saturday that the United States should impose a May 15 deadline on the Iraqi parliament to form "an effective unity government ... or we will immediately withdraw our military." The Democrat also called for "a schedule for withdrawing American combat forces by year's end," saying that doing so will "empower the new Iraqi leadership." Kerry's comments came on the 35th anniversary of his appearance as a Vietnam veteran on Capitol Hill urging an end to that war.

The Australian military suffered its first death Friday, a soldier who shot himself in the head in what's being described as a "tragic accident," according to the military. Defense Minister Brendan Nelson said the soldier's death was not a suicide. (Full story)

British engineer Kenneth Bigley was buried near Falluja after a mock trial, sentencing and beheading in 2004 following his abduction, according to a militant who claims to have been involved. Lawyers for Syrian-born Louai al Sakka said Saturday the militant made the claim and revealed other details "after growing demands of the British media and family." (Details)